What is the Greatest Common Factor of 9805 and 9825?

Greatest common factor (GCF) of 9805 and 9825 is 5.

GCF(9805,9825) = 5

We will now calculate the prime factors of 9805 and 9825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9805 and 9825.

How to find the GCF of 9805 and 9825?

We will first find the prime factorization of 9805 and 9825. After we will calculate the factors of 9805 and 9825 and find the biggest common factor number .

Step-1: Prime Factorization of 9805

Prime factors of 9805 are 5, 37, 53. Prime factorization of 9805 in exponential form is:

9805 = 5¹ × 37¹ × 53¹

Step-2: Prime Factorization of 9825

Prime factors of 9825 are 3, 5, 131. Prime factorization of 9825 in exponential form is:

9825 = 3¹ × 5² × 131¹

Step-3: Factors of 9805

List of positive integer factors of 9805 that divides 9805 without a remainder.

1, 5, 37, 53, 185, 265, 1961

Step-4: Factors of 9825

List of positive integer factors of 9825 that divides 9805 without a remainder.

1, 3, 5, 15, 25, 75, 131, 393, 655, 1965, 3275

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9805 and 9825. The biggest common factor number is the GCF number.
So the greatest common factor 9805 and 9825 is 5.

Also check out the Least Common Multiple of 9805 and 9825